CCITT V. 22 bis modems operating over the telephone network transmit information in the form of symbols identified by both a specific phase shift from one symbol to the next and a particular amplitude relationship. At the receiving end, the transmitted information can be recovered by detecting changes in the phase and amplitude of the incoming signal. Each symbol may typically represent several bits of data.
For a variety of reasons, errors in symbol recognition occur from time to time at the receiving end, often in the form of short error bursts involving fewer than two or three symbols. Forward error correction (FEC) algorithms have been devised to recognize and correct such errors by transmitting extra bits (termed error check bits) derived from a combination of delayed and undelayed data bits. At the receiving end, a similar combination can be used to generate error syndrome bits. The error symdrome bits can be used in a conventional error-correcting logic to recreate the original data train even though some bits may have become garbled during transmission. The FEC algorithm is most efficiently implemented in the form of a convolutional encoder/decoder.
The nature of FEC is such that an error burst of given length can only be corrected after the reception of an error-free guard space whose length is mathematically related to the length of the error burst. In practice, there is one FEC algorithm that can correct a 12-bit burst following a guard space of 191 error-free bits.
Unfortunately, high-speed modems require the use of certain functions which multiply the number of errors caused by the reception of a single erroneous bit. Specifically, the descrambler necessitated by the use of adaptive equalization on poor-quality telephone lines produces as much as three errors for each erroneous bit appearing at its input, while the differential decoder which decodes the received symbols upstream of the descrambler produces at least two errors for each erroneous received bit. Thus, even a one-bit error in a single received symbol typically produces six errors at the output of the descrambler, or half the entire error-correcting capacity of the above-mentioned FEC algorithm. The effectiveness of the FEC would therefore be highly increased if this error multiplication could be avoided.